Factor completely: (5x+1)^(2)(x+2)-(x-3)(5x+1) Answer:

Question

Factor completely:  (5x+1)^(2)(x+2)-(x-3)(5x+1) Answer:

Bytelearn · Accepted Answer

Recognize Common Factor: Recognize that the expression contains a common factor of (5x+1) in both terms. (5x+1)^(2)(x+2)-(x-3)(5x+1) can be rewritten as (5x+1)[(5x+1)(x+2)-(x-3)] by factoring out (5x+1).Distribute and Simplify: Distribute (5x+1) into (x+2) and then distribute the negative sign into (x-3). (5x+1)(x+2) gives 5x^2 + 10x + x + 2, which simplifies to 5x^2 + 11x + 2. -(x-3) gives -x + 3. So, (5x+1)[(5x+1)(x+2)-(x-3)] becomes (5x+1)(5x^2 + 11x + 2 - x + 3).Combine Like Terms: Combine like terms in the expression 5x^2 + 11x + 2 - x + 3. This simplifies to 5x^2 + 10x + 5. So, the expression is now (5x+1)(5x^2 + 10x + 5).Factor Perfect Square Trinomial: Notice that 5x^2 + 10x + 5 is a perfect square trinomial, which can be factored as (5x+5)(5x+5) or (5x+5)^2. So, the expression is now (5x+1)(5x+5)^2.Simplify Common Factor: Recognize that (5x+5) can be simplified by factoring out the common factor of 5, giving us 5(x+1). So, the expression is now (5x+1)(5(x+1))^2.Factor Out Common Factor: Since (5(x+1))^2 is the square of 5(x+1), we can write the expression as (5x+1)(5^2)(x+1)^2. This simplifies to (5x+1)(25)(x+1)^2.Final Factored Form: Finally, we can write the completely factored form of the original expression as (5x+1)(25)(x+1)^2.

Factor completely: $\newline$ $(5 x+1)^{2}(x+2)-(x-3)(5 x+1)$ $\newline$ Answer:

Full solution

More problems from Find derivatives of using multiple formulae

Related topics

Factor completely:\newline(5x+1)2(x+2)−(x−3)(5x+1) (5 x+1)^{2}(x+2)-(x-3)(5 x+1) (5x+1)2(x+2)−(x−3)(5x+1)\newlineAnswer:

Factor completely: $\newline$ $(5 x+1)^{2}(x+2)-(x-3)(5 x+1)$ $\newline$ Answer: